Logical Reasoning Test - 17

Given:

The expression = (5 ÷ 5 of 5 × 2 + 2 ÷ 2 of 2 × 5)

Calculation:

⇒ (5 ÷ (5 of 5) × 2 + 2 ÷ (2 of 2) × 5)

⇒ ((5 ÷ 25) × 2 + (2 ÷ 4) × 5)

⇒ ((5/25) × 2 + (2/4) × 5)

⇒ ((1/5) × 2 + (1/2) × 5)

⇒ (2/5) + (5/2) = (29/10) = 2.9

Given:

The area of the circle is given as 121π sq. cm.

Concept used:

If R unit is the radius of a circle,

then the area of the circle is π × R2 unit²

and the circumference of the circle is 2πR unit

Calculation:

Let the radius of the circle be R.

According to the question,

π × R² = 121π

⇒ R² = 121

⇒ R = 11 (∵ The measure of the radius of a circle can't be negative)

⇒ 2πR = 22π 

∴ The circumference of the circle is 22π cm.

Given:

The required expression: (\(1.0\bar{5}\) ÷ \(0.\overline{95}\) ) × \(0.4\overline{09}\)

Formula used:

\(0.0\bar a= \frac{a}{90}\)

\(0.\overline {aa} = \frac{aa}{99}\)

\(0.a\overline {bc} = \frac{abc-a}{990}\)

Calculation:

The above expression can be written as:

⇒ (\((1 + 0.0\bar{5})\) ÷ \(0.\overline{95}\) ) × \(0.4\overline{09}\)

⇒ (\((1 + \frac{5}{90})\) ÷ \(\frac{95}{99}\) ) × \(\frac{409 - 4}{990}\)

⇒ (\( \frac{90+5}{90}\) ÷ \(\frac{95}{99}\) ) × \(\frac{405}{990}\)

⇒ (\( \frac{95}{90}\) ÷ \(\frac{95}{99}\) ) × \(\frac{405}{990}\)

⇒ (\( \frac{95}{90}\) × \(\frac{99}{95}\) ) × \(\frac{405}{990}\)

⇒ (\( \frac{99}{90}\)) × \(\frac{405}{990}\)

⇒ \(\frac{45}{100}\) = 0.45

∴ The required value of the expression is 0.45.

Calculation:

Remainder = 4

So,

244 - 4 = 240

2052 - 4 = 2048

HCF of 240 and 2048 = 16

⇒ The greatest number = 16 

∴ The greatest number is 16 which divides 244 and 2052 which leaves the remainder 4 in each case.

The correct option is 2 i.e. 16

Given

Length of each side of an equilateral triangle = \(2\sqrt[4]{3}\) cm

Formula used

Area of equilateral triangle = (√ 3/4) × (side)²

Calculation

Area of triangle = (√3/4) × (\(2\sqrt[4]{3}\))²

⇒ (√3/4) × 4 × ((3)^1/4)²

⇒ (√ 3/4) × 4 × √3

⇒ √3 × √3

⇒ 3 cm²

∴ The area of the triangle is 3 cm²

Concept:

Dividend = Divisor × Quotient + Remainder

Calculation:

Let the quotient be = b 

n = 5 × b + 2 

n² = (5b + 2)²

⇒n2 = 25b² + 4 + 2 × 5b × 2 

⇒n2 = 25b2 + 4 + 20b 

⇒n2 = 5(5b2 + 4b) + 4 

∴ When n2 is divided by 5, the remainder will be 4.

Alternate MethodBy Value Putting Method

n/5 → Remainder = 2 

For n = 7, it satisfies the condition. 

⇒ n²/5 = 7²/5 = 49/5 

∴ The remainder (5 × 9 + 4) = 4 

Given:

Base radius = 7 cm

Surface area = 308 cm²

Concept used:

Curved surface area of a cone = π × Radius × Slant Height

Slant height = \( \sqrt{Radius^2 + Height^2}\)

Calculation: 

Let the slant height and the height on the cone be L and H cm respectively.

According to the question,

π × 7 × L = 308

⇒ 22/7 × 7 × L = 308

⇒ L = 14

Hence, Height, H = \(\sqrt{14^2 - 7^2}\) = \(7\sqrt3\) cm

∴ The height of the cone is \(7\sqrt3\) cm.

Given:

The terms are 4x2y, 16xy3, 2x3y3

Calculation: 

Factors of 4x2y = 2 × 2 × x × x × y

Factors of 16xy3 = 2 × 2 × 2 × 2 × x × y × y × y

Factors of 2x3y³ = 2 × x × x × x × y × y × y

Common factors = 2 × x × y = 2xy

∴ HCF is 2xy

Given:

ABCD is a cyclic quadrilateral and  ∠B = 72°

Concept:

Cyclic is a quadrilateral whose all four vertices lie on the circle.

Also, the sum of opposite angles is equal to 180°.

Calculation:

ABCD is a cyclic quadrilateral

⇒ ∠B + ∠D = 180° ( Supplementary angles)

⇒ 72° + ∠D = 180°

⇒ ∠D = 108° 

Given:

The number of sides of the polygon = 24

Concept:

The sum of the interior angle and the exterior angle in 180°

Formula used:

The exterior angle of regular polygon = (360°/n)     Where n = The number of sides of the polygon

Calculation:

Let us assume the interior angle of the polygon be X

⇒ The exterior angle of the polygon = 360/24 = 15°

⇒ X = 180° - 15° = 165° 

∴ The required result will be 165°.